Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
544 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 157 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#16864641 | C2 | semidirect |
| 2. C22×#16864638 | C2 | semidirect |
| 4. #31774145 | C2 | direct (N × H) |
| 5. C2×#22576093 | C2 | semidirect |
| 6. C2×#22576084 | C2 | semidirect |
| 7. C2×#22576080 | C2 | semidirect |
| 8. C2×C22⋊Q8×C271 | C2 | semidirect |
| 12. C2×#16864641 | C22 | semidirect |
| 14. C2×#16864638 | C22 | semidirect |
| 21. #22576093 | C22 | semidirect |
| 22. #22576084 | C22 | semidirect |
| 23. #22576080 | C22 | semidirect |
| 27. C22⋊Q8×C271 | C22 | semidirect |
| 42. C2×C271⋊C8 | D4 | semidirect |
| 76. C271⋊C8 | C2×D4 | semidirect |
| 118. C2×C271 | #468 | semidirect |
| 123. C271 | C2×#468 | semidirect |
| 127. C2×C22⋊Q8 | D271 | semidirect |
| 144. C22⋊Q8 | C2×D271 | semidirect |
| 243. C2 | #31774145 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16864641 | 2 |
| C22×#16864638 | 2 |
| C2×#22576134 | 2 |
| #31774145 | 2 |
| C2×#22576093 | 2 |
| C2×#22576084 | 2 |
| C2×#22576080 | 2 |
| C2×C22⋊Q8×C271 | 2 |
| C2×#468 | 271 |